I gave a lot of reading to found the answer to your question. Every decoment I read does not mention New York as a place where Charles Manson has been.
I could find no evidence that Manson ever lived in New Mexico. ~ Charles Manson was convicted on Mann's Law for transporting a woman from California to New Mexico for purposes of prostitution. As to whether it was Lordsburg or not, I don't know yet.
Charlotte Manson was born on January 21, 1917, in New York, New York, USA.
Joshua Manson was born on January 13, 1971, in New York City, New York, USA.
Janet Manson died on August 10, 1961, in New York City, New York, USA.
Eddy Lawrence Manson was born on May 9, 1919, in New York City, New York, USA.
Helter Skelter
The first blood bank ever invented was in New York, by Charles Drew.
Manson II or David Berkowitz was convicted for the murders or a New York producer and a Madam. He was sentenced to life in Prison without any parole in 1991, in the state of California.
Charles Newirth was born in New York City, in New York, USA.
Charles Guardino was born in 1939, in New York City, New York, USA.
Charles Bauman was born in January 1874, in New York, New York, USA.
Charles James is number 37 on the New York Giants.